Sparsity plays an important role in statistical learning in a high-dimensional scenario, where the underlying parameters are `nearly black' [1]}, implying that only a small subset of the same is non-zero. Several regularization based methods have been proposed in this regard in the literature, that induce sparsity in the models. From a frequentist perspective, such methods include penalization based methods like ridge regression [2]}, lasso [3]}, elastic net [4]}, SCAD [5]}, fused lasso [6]}, [7]}, graphical lasso [8]}, among others; see [9]} for frequentist methods in high dimensions. Bayesian methods in high dimensions have been developed more recently, where sparsity is induced via suitable prior distributions on the parameters. These include spike-and-slab priors [10]}, [11]}, Bayesian lasso [12]}, Bayesian graphical lasso [13]}, and other shrinkage priors like spike-and-slab lasso [14]}, Normal Exponential Gamma [15]}, Horseshoe [16]}, [17]} and other variants like Horseshoe+ [18]} and Horseshoe-like [19]}, Dirichlet-Laplace [20]}, R2-D2 [21]}, among others. Theoretical guarantees of such Bayesian procedures have been developed recently as well. We refer the readers to [22]} for a comprehensive overview of Bayesian methods in a high-dimensional framework.
